On the Dynamics of finite-gap solutions in classical string theory

Nick Dorey, Benoît Vicedo
2006 Journal of High Energy Physics  
We study the dynamics of finite-gap solutions in classical string theory on R x S^3. Each solution is characterised by a spectral curve, \Sigma, of genus g and a divisor, \gamma, of degree g on the curve. We present a complete reconstruction of the general solution and identify the corresponding moduli-space, M^(2g)_R, as a real symplectic manifold of dimension 2g. The dynamics of the general solution is shown to be equivalent to a specific Hamiltonian integrable system with phase-space
more » ... . The resulting description resembles the free motion of a rigid string on the Jacobian torus J(\Sigma). Interestingly, the canonically-normalised action variables of the integrable system are identified with certain filling fractions which play an important role in the context of the AdS/CFT correspondence.
doi:10.1088/1126-6708/2006/07/014 fatcat:dfz7tvev5bgafdwlxn2c2ukggq